In this paper we prove that if f is holomorphic function in one complex variable, whenever k+(n-1)/2 is a non-negative integer, then for any underlying space R the induced function Δf(x)P (x) is left-monogenic, where P is left-monogenic and homogeneous of degree k in R. It is extended the original theorem by Fueter-Sce with an extra monogenic factor P(x) to the higher order case. The work is based on a recent paper by the speaker. © 2011 American Institute of Physics.